Although phononic Weyl nodal line (WNL) states [1]}, [2]} have been proposed in some solid-state materials before, to the best of our knowledge, the phononic DNL states have rarely been predicted by other researchers. More importantly, a natural question is whether two-fold degenerate WNL phonons and four-fold degenerate DNL phonons can coexist in one single solid-state material. In this paper, we answer this question with certainty. For the first time, via first-principles calculations and symmetry analysis, we propose that KCuS with \(Pnma\)  symmetry group is a topological phononic material exhibiting Weyl and DNL phonons. Remarkably, the predicted nodal line phonons are special in that (i) the two-fold degenerate WNL states are formed by the neck crossing point of the hourglass-like dispersion [3]}, [4]}, [5]}, [6]}, [7]}; (ii) the four-fold degenerate DNLs belong to open nodal lines; (iii) the Dirac and Weyl phonon bands are nearly flat and the only “clean” bands in the 5.0–5.2-THz range; (iv) phonon surface states occur only in the [100] and [001] surfaces, unlike those of typical phononic nodal-line materials; and (v) KCuS provides a good platform to study the entanglement between the HWNL phonons and the DNL phonons.
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